Multipole pair resolver



Dec. 30. 1958 G. KRONACHER 2,865,913

MULTIFOLE PAIR RESOLVER Filed June 27, i95 v s Sheets-Sheet 1 INVENTORG. KRONACHE/P ATTORNEY Dec. 30, 1958 G. KRQNACHER 2,855,913

MULTIPOLE PAIR RESOLVER Filed June 27, 1956 5 Sheets-Sheet 2 v a ANGLE(a) VENf G. ONA CHE/P ATTORNEY which have teeth parallel to the axis ofthe device.

United States Patent 2,866,913 MULTIPOLE PAIR RESOLVER Gerald Kronacher,Newark, N. J., assignor to Bell Telephone Laboratories, Incorporated,New York, N. Y., a corporation of New York Application June 27, 1956,Serial No. 594,273 9 Claims. (Cl. 310111) This invention relates toelectromagnetic devices having relatively movable members and, moreparticularly, to generators or resolvers for precision synchro systemswhich convert .displacement, whether rotational or linear, intoelectrical signals.

Synchro devices are utilized for a variety of purposes including theproduction of electrical signals which are the analogs of desiredinformation. As one application, an electrical synchro produces signalsrepresentative of the angular position of a shaft. It is wellestablished that the angular position of a shaft may be represented by asinusoid and for this reason it is convenient to have the synchrogenerate sinusoidally shaped signals with respect to the displacement ofthe shaft. It is apparent that any distortion in the analog signalreduces the accuracy of reproduction of the angular position. One of theprincipal distortions in the analog signal occurs when the mutualinductance between the windings varies with displacement of the shaft ina manner which is not precisely sinusoidal.

Although several methods may be employed to obtain a variable magneticcoupling between windings for electromagnetic devices having relativelymovable members and utilizing transformer action for generating analogsignals, only the two most Widely used methods will be considered here.One method consists in mounting windings on both a stationary member anda controllably movable member of the device. This is the case in theresolver synchro devices, ordinary alternators, and similardeviceshaving movable winding. The second method consists in mounting bothwindings on the stationary member and shaping the movable member so asto control the air gap permeance and thereby the flux path between thewindings. The second method is employed in rotary reluctance devicessuch as high frequency alternators, inductor type frequency changers andsimilar devices requiring variable permeance characteristics.

From an electrical signal generation standpoint, with which we areconcerned here, method 2 is the least complicated and most reliablesince it eliminates the requirement of slip rings necessary to obtainthe induced voltage from the rotor of a method 1 device. For this reasona synchro resolver of the precision here involved is best produced by astructure according to the second method.

A typical rotary reluctance device comprises a ferromagnetic statorprovided with a plurality of pole shoes An excitation winding is woundon each shoe 'with the winding excited from a source of alternatingcurrent of suitable frequency. A second winding is located on each poleshoe and is mounted so as to be linked by the flux produced by theexcitation winding, thereby providing an output signal for the device.The rotor of the device is a ferromagnetic cylinder mounted for rotationwithin the stator, and having a selected number of teeth on its surface.The mechanical rotation of the rotor causes the rotor and stator teethto vary between a condition of alignment and one ,in which the teeth areefiectively in mesh resulting in variation of the reluctance of the airgap under each pole shoe. Consequently, the flux linking the outputwinding varies according to the relative positions of the rotor andstator teeth.

his well established that it is difficult to determine as well as tomachine the tooth contour for either the rotor or stator teeth whichwill produce sinusoidal variation of the air gap permeance with respectto rotor rotation. In order to obtain sinusoidal variation of the poleshoe permeance with respect to the rotor angle, several techniques havebeen applied in the prior art. One technique involves the selection ofthe proper rotor and stator pitch. A second technique employed ischoosing the proper crown width of the rotor teeth. Another practiceinvolves skewing either the rotor or stator teeth with respect to oneanother. The usual rotor or stator has the teeth aligned with the axisof the electromagnetic device. The skewed rotor or stator has the teethlocated on its surface in such a way that the angular-displacement ofthe vertex of each tooth from a reference position varies as a functionof the distance along the axis of rotation of the rotor. In the presentdesigns of movable winding and reluctance type devices only linear skewsare employed, that is, the locus of points on the surface of the rotoror stator as a result of such angular displacement of the tooth is ahelix. Linear skews eliminate certain harmonic flux linkages which occurwith rotor displacement but merely reduce the remaining harmonics.

It is the object of the present invention to increase the accuracy ofconversion from analog information to electrical signals in a synchroresolver or a rotary reluctance device by the elimination of the oddharmonics in the flux linking the rotor and stator as relative rotationoccurs.

In accordance with the present invention, a reluctance type resolver isprovided with a stator core having an even number of pole shoes whichare evenly divided between north and south poles. The pole shoes arearranged with equal numbers of teeth on each pole face and the shoes areequally spaced on the circumference of the stator. The stator core iswound with an excitation winding which is excited from a source ofalternating current of desired frequency and the winding imparts to eachpole shoe the same absolute value of magnetomotive force. A rotor ismounted for rotation within the stator about the axis of the resolverdevice. The rotor core is also arranged with a number of teeth equallyspaced on its surface. The stator and rotor teeth are nonlinearlydisposed with respect to each other. The nonlinear relationship betweenstator and rotor teeth may be described by a group of skews all of whichhave a frequency distribution (as defined for example in Handbook ofProbability and Statistics With Tables, by Burington and May HandbookPublishers, Inc, 1953, chapter III) of relative angular displacementsthe same as the frequency distribution of a sinusoidal curve. The mostconvenient skew, assuming an unskewed stator, is described for a rotorof length L and n teeth by the following equations in cylindricalcoordinates:

2: sin (nX) (1) r being the radial distance to the vertex of the rotortooth cylinder of radius R; X, the angle measured in the base plane froma reference; and Z the distance along the rotor axis measuredperpendicularly from the base plane. For reasons which will become moreapparent hereinafter, the base plane of the cylindrical coordinates isselected at the midpoint of the rotor axis. A similar relationship maybe established for the stator but the rotor equation is chosen tofacilitate the description of the device.

.. .The. number of pole shoes and the number of rotor. teeth areselected in such a way that the poles can be divided into two groupsspaced an integral multiple of :the' pitch of the rotor teethia quarterof this -rotor tooth pole shoes. The coils of a pole shoe pair areconnected .in.opposition and the coil pairs of a poleshoe group areconnected in series. Application of an alternating :current to theexcitation winding produces an alternating flux under each pole shoe.The amplitude of the fiux is :directly proportional to the permeanceunder the pole :shoe. As the rotor is rotated through one fullrevolution,

- the amplitude of the pole shoe fiux goes through it cycles (where n isthe number of rotor teeth as defined above). Due to the effect of thenonlinear skew provided according to the invention, the permeancevariations of a pole shoe pair contain on odd harmonics. The evenharmonic permeance variation is cancelled out as a result of theconnection in opposition of the sensing coils of the pair. The result isthat the amplitude of the signal appearing in the output circuit variestruly sinusoidally as a function of rotor rotation. ment between thepole shoe groups, the amplitudes of the signals appearing in the outputcircuits are displaced from each other by one-quarter cycle or 90degrees.

The above and other features of the invention will be described in thefollowing detailed specification taken in connection with the drawings,in which:

Fig. 1 is an isometric drawing of a resolver according to the inventionpartially broken away to show the arrangement of the rotor and statorteeth;

Fig. 2 is an electrical circuit diagram of one embodiment showing aresolver which produces two sinusoidal voltages that are displacedone-quarter of a cycle; Fig. 3 includes graphs of the induced voltagedeveloped in an output circuit as a function of the rotor angle Wlil'lcurve (a) representing the voltage before interconnection of sensingcoils for a rotor without skewed teeth; (b) represents the voltage afterinterconnection of sensing co11s for a rotor without skewed teeth; andrepresents the voltage after interconnection of sensing coils with arotor having teeth skewed according to the sinusoidal distribution ofthe invention;

Fig. 4 is an isometric drawing of a suitable rotor for use 1n a synchroaccording to the invention but having only a limited number of teethshown to facilitate the showing of the sinusoidally distributed skew;and the cylindrical coordinate system for describing the shape of theskew;

Fig. 5 is a graph of a sinusoidally skewed tooth placed on the developedrotor surface with the abscissa representmg the angular displacement ofa point on the tooth measured from a reference in a plane parallel to afirst plane lying midway along the rotor axis; the ordinate indicatingthe axial displacement of the same point on the tooth from theintersection of the first plane and a second plane including the rotoraxis and being normal to the first plane;

Fig. 6 is a frequency distribution of the rotor teeth angular rotationfor a sinusoidally shaped skew; and

Fig. 7 is a graph of a nonlinear skew that produces the same effect onthe odd harmonics of the air gap flux as a sinusoidal skew.

In Fig. 1 a resolver device is shown as comprising a stationary memberor stator 1 having eight pole shoes (2 through 9) each with a pluralityof inwardly projecting members or teeth 10. These pole shoes are equallyspaced around the circumference of the stator. As shown in theelectrical circuit of Fig. 2, the stator is provided Because of thespatial displace- .with a single phase induction winding 11 ofsuificient turns to develop predetermined magnetomotive forces of equalamounts at each pole shoe with pole shoes 3, 4, 5, 6 being wound toproduce north poles for positive input currents and pole shoes 7, 8, 9,and 2 being wound to produce south poles for positive input currents. Asource of alternating current 12 of desired frequency is connectedacross the terminals of winding 11.

A sensing coil 13 (see Fig. 2) is placed on each pole shoe, and ismounted in such a manner as to be linked with the magnetic fieldproduced by winding 11. The coils 13 of pole shoes 3, 5, 7, and 9 areinterconnected to form an output circuit A for the pole shoe group. Theremaining coils 13, i. e., those on poles 2, 4, 6, and 8, are similarlyinterconnected to form a second output circuit B from the second poleshoe group. In the first group, sensing coils 13 on poles 3 and 7 areconnected in series to form a first coil pair 3-7. Likewise, the sensingcoils .13 on poles 5 and 9 are connected in series to form a second coilpair 5-9. The first and second coil pairs of the first group of polesare connected in opposition to produce an output which is the differencebetween the induced voltage for poles 3-7 and 5-9. In the second groupof poles, sensing coils 13 on poles 2 and 6 are connected in series toform a first coil pair 2-6. Similarly, the sensing coils 13 on poles 4and 8 are connected in series to form a second coil pair 4-8. The firstand second coil pairs of the second group of poles are connected inopposition to produce an output which is the difference between theinduced voltages for poles 2-6 and 4-8.

A rotor 14 is provided for the resolver and is mounted for rotationwithin the stator 11 by any of the well known methods employed inelectrical machinery. The rotor mounting structure in Fig. l isschematic and is chosen only to permit a clear showing of the stator androtor core structures. As shown, the rotor has a plurality of outwardlyprojecting members or teeth 15 equally spaced on its periphery.

It is apparent that as the rotor is rotated the stator and rotor teethmove between conditions of alignment and mesh. The number of stator androtor teeth is selected so that the pole shoes of a group are spaced anintegral multiple plus half a rotor pitch. Although the increment ofrotor pitch may be either positive or negative, it may not be both inthe same structure and is here taken as positive for convenience inexposition. A rotor pitch is defined as the circumferential distancebetween crown points of contiguous teeth. The second group of pole shoeshas the same spacing as the first group of pole shoes but the group isspaced from the first group an integral multiple plus a quarter of arotor pitch for reasons which will become more apparent hereinafter.

Referring to Fig. 2, it is evident that in the position shown theselected number of rotor and stator teeth results in alignment of teethfor poles 2 and 6 and meshing of the teeth for poles 4 and 8 both poleshoe pairs being in the first group of pole shoes. It is also evidentthat a similar relative spacing will exist between the stator and rotorteeth for the second group of pole shoes.

The flux produced by energizing the excitation winding 11 links thesensing coils 13 as it passes through the air gap and rotor structure ofthe device. For the first group of sensing coils on poles 3, 5, 7, and 9shown on Fig. 3, the flux travels out from pole 3 which is of northpolarity (as mentioned hereinbefore) and then through the air gap torotor structure 4. Thence, it travels into pole 7 which is of southpolarity (as mentioned herein before) via the air gap and then throughthe stator frame to pole 3. A similar flux path may be described forpoles 5-9. The reluctance or flux resistance in the flux path isproportional to the flux path length divided by the flux path area andthe constant of proportionality is defined as reluctivity. Thereluctivity for air is given a value of unity whereas that for the ironportion of the circuit is lower and depends on the characteristics ofthe iron. The reluctance of the flux path is obtained by instantaneouslysumming the indilidual reluctances for the air gap and iron portions ofa flux path. It is apparent that the interaction of the rotor and statorteeth causes the reluctance of the air gap and iron flux paths to passthrough n variations for each full rotation of the rotor. A curve may beplotted of the flux variation under a pole shoe as a function of rotorangle and the curve will depend principally upon the shape of the statorand rotor teeth. Fig. 3(a) illustrates the flux versus rotor angle forpole pairs 3-7 and 5-9 which are spaced an integral multiple of thepitch of the rotor teeth plus half a rotor pitch. It will be recalledfrom Fig. 2 that one pole pair of a group comprises pole shoes withopposite polarities but having the same interaction of rotor and statorteeth. The other pole pair of the group also comprises pole shoes withopposite polarities and the same interaction of rotor and stator teeth,but where the interaction is inverted with respect to that of the firstpole pair. Thus, the curve of flux variation for a pole group resemblesa continuous series of sinusoidal half cycles. be noted, however, thatthe efiect of the skew has not been considered in determining the curveof flux distribution.

It was previously stated that the sensing coils on a pole pair arelinked by the flux produced by the pole pair and the coils are connectedin series. The sensing coil pairs of a group of pole shoes are connectedin opposition with the result that Fig. 3(b) indicates the inducedvoltage in an output circuit for the sensing coils of a pole group. Thewave shape of the induced voltage is identical above and below theabscissa and well known wave analysis techniques indicate that in suchcases the even harmonics of the flux variation with respect to rotorangle are eliminated.

However, the odd harmonics of the flux variation are present and it willnow be shown that a sinusoidally distributed skew placed on the rotorsurfaces according to the invention can eliminate the effects of theseharmonics. The combined effect of connecting pole pairs of a group inopposition and the sinusoidal skew produces an output voltage thatconsists entirely of the fundamental of the flux variation in the airgap with respect to the rotor angle. v

The shape of the skew in the preferred embodiment of the invention is inthe form of a sinusoid. Fig. 4 indicates the rotor structure and teethin more detail but for purposes of better illustration only a few of theteeth are shown. The skew is properly described with -respect to asystem of cylindrical coordinates wherein X the base plane, is takennormal to the rotor axis at its midpoint, this location being chosen forreasons which will become apparent hereinafter. Z is a reference planewhich includes the resolvers axis, and it is normal to the 7 It should Xplane. The curves made by the rotor teeth are functions of r the radiusof. the. cylinder contiguous tothe vertex of the rotor teeth; X. theangular displacement from a reference of points on a tooth measured in aplane parallel to the base plane X and Z the distance in the Z plane ofcorresponding points from the intersection of the X and Z planes. Sincethe radius of the rotor teeth cylinder is constant, the sinusoidal skewmay be accurately described as functions of the Z and X parameters, andEquation 1 previously given defines the preferred skew with respect tothe cylindrical cordinate system shown in Fig. 4. The flux'variationunder pole shoes 37 and 5-9, as shown in Fig. 3(1)), describes a cosinefunction of (n9) since the flux passes through it cycles for a rotorangle 0 of 277 radians. 0 is the angular rotation imparted to the rotor14 from an outside source whereas X is the structural displacement ofpoints on a rotor tooth from a reference. Without rotor rotation "thedescribed embodiment'would be no -more than a transformer. A. Fourierseries may bewritten forthe iiux variation as follows:

131 1 008 U-FAQ cos (3n0)+ +Ancos mflH- In the Fourier series, Arepresents the maximum amplitude of a harmonic of order ,u. Since allharmonics in the flux variation are odd, they are described by thefollowing relation where m is any positive integer:

skewed per unit= i) cos (5) n=1, The total flux of pole shoes 3-7 and5-9 is obtained by integrating Equation 5 over the rotor length L:

2n The value of all may be found in terms of x to permit integration ofEquation 4 by differentiating Equation 1 and substituting into Equation4 as follows:

alga-sears The bracketed expressions in Equation reduce to zero sincethere is no difference between the angular quantities. Thus, the thirdharmonic flux is zero. It may be readily refinements established thatsubstitutionof all odd harmonics except a the fundamental reducesEquation 15 to zero. The magnitude of the fundamental of the Fourierseries is found by letting ,u.=l and substituting into Equation 12 3 sgcos-ma 20 Equation 12"indicat'es that the magnitudeof the flux, underpole shoe pairs 3-7, 5-9 as a result of sinusoidally skewing the rotorwill vary sinusoidally as a function of rotor rotation.

Since the variation of air ga'p'fiux under each pole shoe pairissinusoidal with rotor rotation then Fig. 4(a) indi'cates' the air gapflux variation for a pole group with the effect of the sinusoidal skewtaken into consideration. It will be recalled that the resolver has twopole groups which are displaced from each other by an integral multipleplus a quarter of a rotor pitch. It may be shown by similar mathematicalprocedures that the flux variation for the second poleshoe group issinusoidal but due to the spatial displacement between the groups thereis a quarter cycle variation'or degrees between thefiux linking the coilgroups.

There are other nonlinear skews which will eliminate generation of oddharmonics in the air gap flux from the movement of the rotor. If thesinusoidally skewed rotor is considered as comprising an infinite numberof laminations,- then the summation of the flux associated with eachlamination is without odd harmonics as the rotor turns through an angleequal to that subtended by the tooth pitch. It will be recognized thatrearranging the axial occurrence of each lamination but preserving theangular orientations of each will not alter the summation of the flux asfound for a sinusoidally skewed rotor. In addition, the frequencydistribution of the angular displacements for the rearranged rotorlaminations is the same as the frequency distribution of angulardisplace ments for a sinusoidally skewed rotor. A frequency distributionis here represented by a graph in which the abscissa is angulardisplacement and the ordinate for a particular abscissa is the portionof the total rotor length for which the indicated angular displacementof the teeth with respect to a reference as previously defined exceedsaminimum displacement but is less than the displacement indicatedfor-that abscissa. Hence, there are an infinite number of nonlinearskews which may be employed to eliminate odd harmonics in the air gapflux since eachrearrangement of the'order of occurrence of laminationsof particular angular displacements is a possiblenonlinear skew.However, all nonlinear skews have the same-frequency distribution ofangular displacement as a sinusoidal skew.

In Fig. 5, the maximum angular displacement of a rotor tooth is shown asskew is shown and the equation for the curve is as follows:

)\(--[[]2h, a)=% sin na+% 21 It will be r'ecalledthat n is thenumber ofrotor teeth on the'rotor surface.

'9 In Fig. 7,- a nonlinear skew is shown which appears quite differentfrom a sinusoidal skew. The frequency distribution of angulardisplacement for the skew is obtained by arbitrarily selecting thevarious is and determining the its associated with each a. For a;themagnitude of R represents the portion of the total rotor lengthangularly displaced more than -lI/2n and less than with respect to'themedian displacement. Likewise, it, represents the portion of the totalrotor'length angularly displaced for ar For a the portion of the totalrotor length angularly displaced is given by x 44, since each laminationis rotated more than II/2n but less than a A plot of the As against theas for Fig. 7 is shown on Fig. 6 and it is evident that the equation ofthe curve is same as that for Fig. 6. Hence, the skew shown in Fig. 7will eliminate odd harmonics in the air gap flux as the rotor turns.

The operation of the resolver occurs when the excitation winding isenergized from source 12, and rotor 14 is rotated. As the rotor rotatesthe air gap flux which links sensing coils 13 is caused to vary as aresult of the interaction of the stator and rotor teeth. It should beunderstood that the rotor-stator teeth flux variationis superimposed onthe time variation of the flux which originates from the source ofalternating current 12.

The nonlinear skew having a frequency distribution curve the same asEquation 21 eliminates odd harmonics in the air gap fiux as the rotorturns through an angle equal to that subtended by the tooth pitch. Theeven harmonics in the air gap flux as the rotor turns are cancelled outas a result of the connection of sensing coils 13 for a pole pair inopposition. The voltage appearing in each output circuit is a modulatedcarrier of the frequency provided by source 12, and the envelope of thecarrier is without odd or evenharmonics. The, output voltage maytherefore be employed very precisely to represent the angular positionof the rotor.

It is to be understood that the invention has been described inconnection with specific embodiments, and other modifications andembodiments will readily occur to one skilled in the art withoutdeparting from the spirit of the invention.

What is claimed is:

1. In an electromagnetic device for generating substantially puresinusoidal voltages a stator, a rotor mounted for rotation therein, saidrotor having a plurality of teeth equally spaced about its periphery,the angular po sitions of points on an individual tooth as measured fromthe reference formed by the intersection of a plane including the rotoraxis and a cylinder having the same axis and tangent to the vertices ofsaid. rotor teeth, being a sinusoidal function of the distance along therotor measured parallel to said axis, at least a pair of poles formed onsaid stator and having teeth parallel to said axis, said poles beingspaced an integral multiple plus halt a rotor tooth pitch, means forestablishing a single phase sinusoidal flux pattern in said stator,means for imparting mechanical rotation to said rotor, and meansinductively coupled to said flux pattern to provide an output free ofeven harmonics as the rotor turns.

2. In an electromagnetic device for generating substantially puresinusoidal voltages a stator, a rotor mounted for rotation therein, saidrotor having a plurality of teeth equally spaced about its periphery theangular positions of points on an individual tooth, as measured from thereference formed by the intersection of a plane including the rotor axisand a cylinder having the same axis and tangent to the vertices of saidrotor teeth, being a sinusoidal function of the distance along the rotormeasured parallel to said axis, at least two pairs of poles formed onsaid stator and having teeth parallel to said axis, the poles of eachpair being spaced an integral multiple plus half a rotor tooth pitch andthe angular separation between poles-of different groups being anintegral multiple plus one-quarter rotor tooth pitch,

' meansfor establishing a single phase 'sinusoid'al'fiux pat tern insaid stator, means for imparting'mechanical rotation to said rotor, andmeans inductively coupled to said flux pattern to provide an'output freeof even harmonics as the rotor turns.

3. In an electromagnetic device for generating substantially puresinusoidal voltages a stator, a rotor mounted for rotation therein, saidrotor having a plurality of teeth equally spaced aboutits periphery theangular positions of points in an individual tooth, as measured from thereference formed by the intersection of a plane including the rotor axisand a cylinder having the same axis and tangent to the vertices of saidrotor teeth, being a sinusoidal function of the distance along the rotormeasured parallel to said axis, at least a pair of poles formed'on saidstator and having teeth parallel to said axis, said poles being spacedan integral multiple plus half a rotor tooth pitch, means forestablishing a single phase sinusoidal flux pattern in said stator,means for imparting mechanical rotation to said rotor, a sensing coilmounted on each of said poles for inductive coupling to said fiuxpattern,- and means serially interconnecting said coils to provide anoutput proportional to the difference of the voltages induced therein.

4. In an electromagnetic device for generating substantially puresinusoidal voltages a stator, a rotor mounted for rotation therein, saidrotor having a plurality of teeth equally spaced about its periphery theangular positions of points in an individual tooth, as measured from thereference formed by the intersection of a plane including the rotor axisand a cylinder having the same axis and tangent to the vertices of saidrotor teeth, being a sinusoidal function of the distance along the rotormeasured parallel to said axis, at least a pair of poles formed on saidstator and having teeth parallel to said axis, said poles being spacedan integral multiple plus half'a rotor tooth pitch, means forestablishing a single phase sinusoidal flux pattern in said stator,means for imparting mephanical rotation to said rotor, a sensing coilmounted on each of said poles for inductive coupling to said fluxpattern, and means serially interconnecting the coils of each of saidpaired poles to provide individual outputs proportional to thedifference of the voltages induced therein.

5. In an electromagnetic device for generating substanin m;

where Z is the distance along the rotor measured parallel to said rotoraxis from a reference plane X normal to said rotor axis at its midpointand L is the total length of said rotor, at least a pair of poles formedon said stator and having teeth parallel to said axis, said poles beingspaced an integral multiple plus half a rotor tooth pitch, means forestablishing a single phase sinusoidal flux pattern in said stator,means for imparting mechanical rotation to said rotor, and meansinductively coupled to said flux pattern to provide an output free ofeven harmonics.

6. In an electromagnetic device for generating substantially puresinusoidal voltages a stator, a rotor mounted for rotation therein, saidrotor having n teeth equally spaced about its periphery, thedistribution of angular displacement of elements on a rotor tooth vertexthe same as a sinusoid, at-least a pair of poles formed on said statorand having teeth parallel to the said axis, said poles being spaced anintegral multiple plus half a rotor tooth pitch, means for establishinga single phase sinusoidal flux patternyin said stator, means forimpartingmechanie cal rotationrto said rotor, and means inductivelycoupled tosaid flux pattern to, providesanoutput.

7. .In an electromagnetiedevice for generating substantially puresinusoidal voltages a stator, a rotormounted for'rotation therein, saidrotor having 11 teeth equally spacedabout its periphery, thedistribution of angular displacements of elements on a rotor toothvertex being defined by sin n z+ Where )r equals the portion of thetotal rotor length for which the angular displacements of the rotortooth vertices. are more than and less than or measured from a referenceformed by the intersection of a plane including the rotor axis and acylinder having the same axis and tangent to the vertices of said rotorteeth, at least a pair of poles formed onsaid stator and having teethparallel to said axis, said poles beingspaced an integral multiple plushalf a rotor tooth pitch, means for establishing a single phasesinusoidal flux pattern in said stator, means for imparting mechanicalrotation to said rotor, and means inductively coupled to said fluxpattern to provide an output.

8. In anelectromagnetic device for generating substantially puresinusoidal voltages a stator, a rotor mounted for rotation therein, saidrotor having n teeth equally spaced about its periphery, thedistribution of angular displacements of elements on a rotor toothvertex being defined by sin i10t+ /2 where x equals the portion'of thetotal rotor length for which the angular displacements of-the rotortooth vertices are more than der having the same axis and tangent to thevertices of said rotor teeth, at least a pair of poles formed on saidstator. and havingwteeth parallel to said axis, said poles heingspacedan integral multiple plus halfwa rotor tooth pitch, means forestablishing a single phase sinusoidal flux patternin saidstator, means}for imparting mechanical rotationtosaid rotor, and means inductivelycoupledto saidflux pattern to provide an output free ofeven harmonies. pv

9. In anelectromagnetic device for generating substantially puresinusoidal voltages a stator, a rotor mounted for rotation therein, saidrotor having a plurality of teeth equall spaced about. its periphery,the distribution of angular displacements of elements on aroto-r toothvertex being defined by 5i11.n0z+ /2 where equals the portion of thetotal rotor length for which the angular displacements of the rotortooth vertices are'more than and less than a measured from a referenceformed by the intersection of a plane including the rotor axis and acylinder having the same axis and'tangent to the vertices of said rotorteeth", .at least two pair of poles formed on said stator and havingteeth parallel to said axis, the poles ofeach pair being spaced anintegral multipleplus half a rotor tooth pitch and the angularseparation between poles of ditferent groups being an integral multipleplus onequarter rotor tooth p'it ch,,me ans for establishing a singlephase sinusoidal flux pattern in said stator, means for impartingmechanical rotation to said rotor, a sensing coil mounted on each ofsaid poles for inductive coupling to said flux pattern, and meansserially interconnecting the coils of each ofsaid paired poles toprovide individual outputs proportional to the difference of thevoltages induced therein.

Glass Nov. 22, 1949 Herr Aug. 26, 1952

